Question

How do you find a numerical value of one trigonometric function of x given `cscx=sinxtanx+cosx`?

Answer 1

`:.x=pi/4+pin`

Explanation:

`cscx=sinxtanx+cosx`

`1/sinx = sinxsinx/cosx+cosx`

`1/sinx=sin^2x/cosx+cosx`

`1/sinx=(sin^2x+cos^2x)/cosx`

`1/sinx=1/cosx`

`1=1/cosx*sinx`

`1=sinx/cosx`

`1=tanx`

`tan^-1 1=x`

`:.x=pi/4+pin`